Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

Julien Petit, Timoteo Carletti, Malbor Asllani, Duccio Fanelli
2015 Europhysics letters  
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the
more » ... lity are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.
doi:10.1209/0295-5075/111/58002 fatcat:vti4mbnkvnh3la4smo2aqjjsem